Title:
Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time

Abstract: We introduce the smoothed analysis of algorithms, which is a hybrid of the
worst-case and average-case analysis of algorithms. In smoothed analysis, we
measure the maximum over inputs of the expected performance of an algorithm
under small random perturbations of that input. We measure this performance in
terms of both the input size and the magnitude of the perturbations. We show
that the simplex algorithm has polynomial smoothed complexity.